Investigators have noted for long that proteins adsorb on solid surfaces non-uniformly. This inhomogeneity shows up in form of small clusters. by confining the analysis to dilute systems where proteins adsorb irreversibly on a charged surface and show no surface mobility, some common causes for clustering have been ruled out. These are clustering in the bulk as well as reformation or phase changes in the adsorbed phase. An approximate solution to the non-equilibrium double layer when the adsorption is diffusion limited is given first. This is followed by a linear stability analysis which shows that adsorption is indeed unstable to small perturbations. Small disturbances in the positions of the proteins near the surface are overcome by electrostatic forces of attraction to the substrate. Indeed the rate of growth of the disturbances is proportional to the product of the charge of the protein and the surface charge density of the substrate.